Hello, just 1 quick question ... there was in the years 1840 -1850 a main diocesis in genova ? where the people use to make the birth acts and get married? like now when you have a baby you go to the municipality to declare him and make it legal? and if so, this still exist?

Darig,
from Concilio di Trento (1545- 1563) to 1820 church records were the only one to be registred.
After 1820 there were two registration, one to the church and one to the comune (the second one is a legal declaration) about birth, marriage and death record.
If you don't find the church record you are looking for you can contact Diocese of Genova

The birth act (actually the Baptism act) is kept by the Parish only; sometimes, but only sometimes, it is also in the archive of the Diocese; locating a parish of 1840 can be difficult because you can only find list of today's parishes and of course the number has changed together with the population (merging small ones and creating new ones).
Italian Civil records begin in 1866. Prior to that all states (and cities) had different rules.
good luck!
Marco, Milano, Italia